Question

What transformation is represented by the rule (x, y)→(x, −y) ?

rotation of 180° about the origin

reflection across the x-axis

rotation of 90° counterclockwise about the origin

reflection across the y-axis

Answer 1

Reflection across the x-axis.

Explanation:

Use `color(blue)"squared paper"` and plot some coordinate points.

For example.

: `(2,3)" and " (-3,-2)" and reflect them in the x-axis."`

You should obtain the following results.

`(2,-3)" and " (-3,2)" respectively"`

Note that the x-coordinate remains unchanged, while the y-coordinate is the negative of the original point.

In general this can be expressed as

Under reflection in the x-axis `(x,y)to(x,-y)`